Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-8x-3y &= 8 \\ -x-y &= -4\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-x = y-4$ Divide both sides by $-1$ to isolate $x$ $x = {-y + 4}$ Substitute this expression for $x$ in the first equation. $-8({-y + 4}) - 3y = 8$ $8y - 32 - 3y = 8$ Simplify by combining terms, then solve for $y$ $5y - 32 = 8$ $5y = 40$ $y = 8$ Substitute $8$ for $y$ in the top equation. $-8x-3( 8) = 8$ $-8x-24 = 8$ $-8x = 32$ $x = -4$ The solution is $\enspace x = -4, \enspace y = 8$.